where \(\gamma \)  is a tunable stepsize and \(\mathbf {x}_i^0=\mathbf {x}_i, \widehat{\mathbf {x}}_i^0=0\) . We owe the success of algcon1 to the compression on the innovation \(X^k-\widehat{X}^k\) , where \(\widehat{X}^k\)  can be viewed as an estimate of \(X^k\) , and reduces to \(X^k\)  if the compression error is zero. Since the fixed points of \(\widehat{\mathbf {x}}_i^k\)  and \(\mathbf {x}_i^k\)  in algcon1 are both \(\bar{\mathbf {x}}\) , the innovation as well as its compression error is expected to vanish if nodes have achieved consensus. In this view, we obtain a strictly better convergence rate for algcon1 than that of [1]} in the following theorem, the proof of which is relegated to adx1.
